Constructive method for finite-dimensional observer-based control of 1-D parabolic PDEs

Balas, 1988, Finite-dimensional controllers for linear distributed parameter systems: exponential stability using residual mode filters, Journal of Mathematical Analysis and Applications, 133, 283, 10.1016/0022-247X(88)90401-5 Baudouin, 2019, Stability analysis of a system coupled to a heat equation, Automatica, 99, 195, 10.1016/j.automatica.2018.10.021 Christofides, 2001 Coron, 2004, Global steady-state controllability of one-dimensional semilinear heat equations, SIAM Journal on Control and Optimization, 43, 549, 10.1137/S036301290342471X Curtain, 1982, Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input, IEEE Transactions on Automatic Control, 27, 98, 10.1109/TAC.1982.1102875 Fridman, 2014 Harkort, 2011, Finite-dimensional observer-based control of linear distributed parameter systems using cascaded output observers, International Journal of Control, 84, 107, 10.1080/00207179.2010.541942 Karafyllis, 2019, Sampled-data observers for 1-D parabolic PDEs with non-local outputs, Systems & Control Letters, 133, 10.1016/j.sysconle.2019.104553 Karafyllis, 2018, Sampled-data boundary feedback control of 1-D parabolic PDEs, Automatica, 87, 226, 10.1016/j.automatica.2017.10.006 Katz, R., & Fridman, E. (2020). Finite-dimensional observer-based controller for linear 1-D heat equation: an LMI approach. In 21st IFAC world congress. Berlin. Katz, 2020, Boundary delayed observer-controller design for reaction-diffusion systems, IEEE Transactions on Automatic Control, 10.1109/TAC.2020.2973803 Krstic, 2008 Lasiecka, 2000 Orlov, 2017, On general properties of eigenvalues and eigenfunctions of a Sturm–Liouville operator: comments on “ISS with respect to boundary disturbances for 1-D parabolic PDEs”, IEEE Transactions on Automatic Control, 62, 5970, 10.1109/TAC.2017.2694425 Orlov, 2004, Robust stabilization of infinite-dimensional systems using sliding-mode output feedback control, International Journal of Control, 77, 1115, 10.1080/0020717042000273078 Pazy, 1983 Prieur, 2018, Feedback stabilization of a 1-D linear reaction–diffusion equation with delay boundary control, IEEE Transactions on Automatic Control, 64, 1415, 10.1109/TAC.2018.2849560 Selivanov, 2018, Delayed point control of a reaction–diffusion PDE under discrete-time point measurements, Automatica, 96, 224, 10.1016/j.automatica.2018.06.050 Selivanov, 2019, Boundary observers for a reaction-diffusion system under time-delayed and sampled-data measurements, IEEE Transactions on Automatic Control, 64, 3385, 10.1109/TAC.2018.2877381 Tucsnak, 2009 Van Loan, 1977, The sensitivity of the matrix exponential, SIAM Journal on Numerical Analysis, 14, 971, 10.1137/0714065 Wei, 2019, A PDE approach to deployment of mobile agents under leader relative position measurements, Automatica, 106, 47, 10.1016/j.automatica.2019.04.040